Geodesic
Estimates of the derivatives, with respect to the initial data, of the expectation of a solution of a stochastic equation on a manifold
Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 167-189 
G. V. Nosovskii. Estimates of the derivatives, with respect to the initial data, of the expectation of a solution of a stochastic equation on a manifold. Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 167-189. http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a8/
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The author obtains estimates of the first two derivatives, with respect to the initial data, of the solution of a stochastic differential equation given on a smooth Riemannian manifold $M$. The case where $M$ is a nonsingular surface in a Riemannian space is studied separately. Bibliography: 11 titles.

[1] Ito K., “Stochastic differential equations in a differentiable manifold”, Nagoya Math. J., 1 (1950), 35–47 | MR | Zbl

[2] Krylov N. V., Upravlyaemye protsessy diffuzionnogo tipa, Nauka, M., 1977, 400 pp. | MR

[3] Dubrovin B. L., Novikov S. D., Fomenko L. T., Sovremennaya geometriya. Metody i prilozheniya, Nauka, M., 1979, 760 pp. | MR

[4] Ikeda N., Watanabe S., Stochastic differential equations and diffusion processes, Amsterdam, Tokyo, 1981, 464 pp. | MR

[5] Meyer P. A., “Geometrie stochastique sans larmes”, Seminarie de Prob., Lect. Notes Math., XV, 1981, 44–102 | MR | Zbl

[6] Liptser R. Sh., Shiryaev A. N., Statistika sluchainykh protsessov, Nauka, M., 1974, 696 pp. | MR | Zbl

[7] Krylov N. V., Nelineinye ellipticheskie i parabolicheskie uravneniya vtorogo poryadka, Nauka, M., 1985, 376 pp. | MR

[8] Blagoveschenskii Yu. N., Freidlin M. I., “Nekotorye svoistva diffuzionnykh protsessov, zavisyaschikh ot parametra”, Dokl. AN SSSR, 138 (1961), 508–511 | MR | Zbl

[9] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, t. 2, Nauka, M., 1981, 416 pp.

[10] Khirsh M., Differentsialnaya topologiya, Mir, M., 1979, 280 pp. | MR | Zbl

[11] Belopolskaya Ya. I., Daletskii Yu. L., “Uravneniya Ito i differentsialnaya geometriya”, UMN, 37:3 (1982), 95–142 | MR